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Approximation of fractals by manifolds and other graph-like spacesFeb 08 2018We define a distance between energy forms on a graph-like metric measure space and on a discrete weighted graph using the concept of quasi-unitary equivalence. We apply this result to metric graphs and graph-like manifolds (e.g. a small neighbourhood ... More

Dimension dependence of factorization problems: Hardy spaces and $SL_n^\infty$Feb 08 2018Given $1 \leq p < \infty$, let $W_n$ denote the finite-dimensional dyadic Hardy space $H_n^p$, its dual or $SL_n^\infty$. We prove the following quantitative result: The identity operator on $W_n$ factors through any operator $T : W_N\to W_N$ which has ... More

Some counterexample on recent algorithms constructed by the inverse strongly monotone and the relaxed $(u, v)$-cocoercive mappingsFeb 08 2018In this short paper, we show that a fundamental part of the proof that has used to construct some iterative algorithms by the inverse strongly monotone and the relaxed $(u, v)$-cocoercive mappings, is invalid. In the other words, we prove that several ... More

B-metric spaces, fixed points and Lipschitz functionsFeb 08 2018The paper is concerned with b-metric and generalized b-metric spaces. One proves the existence of the completion of a generalized b-metric space and some fixed point results. The behavior of Lipschitz functions on b-metric spaces of homogeneous type, ... More

Order continuous operators on pre-Riesz spaces and embeddingsFeb 07 2018We investigate properties of order continuous operators on pre-Riesz spaces with respect to the embedding of the range space into a vector lattice cover or, in particular, into its Dedekind completion. We show that order continuity is preserved under ... More

Generalized localization operators: Cohen's class and trace class operatorsFeb 07 2018We study generalized localization operators from the perspective of Werner's operator convolutions which allows us to extend known results from the rank-one case to trace class operators. The idea of localizing a signal to a domain in phase space is approached ... More

Gundy-Varopoulos martingale transforms and their projection operators on manifolds and vector bundlesFeb 07 2018This paper proves the $L^p$ boundedness of generalized first order Riesz transforms obtained as conditional expectations of martingale transforms \`a la Gundy-Varopoulos for quite general diffusions on manifolds and vector bundles. Several specific examples ... More

On fractional Hardy inequalities in convex setsFeb 07 2018We prove a Hardy inequality on convex sets, for fractional Sobolev-Slobodecki\u{\i} spaces of order $(s,p)$. The proof is based on the fact that in a convex set the distance from the boundary is a superharmonic function, in a suitable sense. The result ... More

On the sum of projectors onto convex setsFeb 07 2018The projector onto the Minkowski sum of closed convex sets is generally not equal to the sum of individual projectors. In this work, we provide a complete answer to the question of characterizing the instances where such an equality holds. Our results ... More

A note on supercyclic operators in locally convex spacesFeb 06 2018We treat some questions related to supercyclicity of continuous linear operators when acting in locally convex spaces. We extend results of Ansari and Bourdon and consider doubly power bounded operators in this general setting. Some examples are given. ... More

Strong pseudo-amenability of some Banach algebrasFeb 06 2018In this paper we introduce a new notion of strong pseudo-amenability for Banach algebras. We study strong pseudo-amenability of some Matrix algebras. Using this tool, we characterize strong pseudo-amenability of $\ell^{1}(S)$, provided that $S$ is a uniformly ... More

Boundary representations of $λ$-harmonic and polyharmonic functions on treesFeb 06 2018On a countable tree $T$, allowing vertices with infinite degree, we consider an arbitrary stochastic irreducible nearest neighbour transition operator $P$. We provide a boundary integral representation for general eigenfunctions of $P$ with eigenvalue ... More

Shorted operators and minus orderFeb 06 2018Let $\mathcal{H}$ be a Hilbert space, $L(\mathcal{H})$ the algebra of bounded linear operators on $\mathcal{H}$ and $W \in L(\mathcal{H})$ a positive operator. Given a closed subspace $\mathcal{S}$ of $\mathcal{H}$, we characterize the shorted operator ... More

Schauder bases and the decay rate of the heat equationFeb 06 2018We consider the classical Cauchy problem for the linear heat equation and integrable initial data in the Euclidean space $\mathbb{R}^N$. In the case $N=1$ we show that given a weighted $L^p$-space $L_w^p(\mathbb{R})$ with $1 \leq p < \infty$ and a fast ... More

Localizing Weak Convergence in $\boldsymbol{ L_\infty}$Feb 06 2018For a general measure space $(X, \sL, \l)$ the pointwise nature of weak convergence in $\Li$ is investigated using singular functionals analogous to $\d$-functions in the theory of continuous functions on topological spaces. The implications for pointwise ... More

Properties of the Space of Sections of Some Banach BundlesFeb 06 2018One shows for Banach bundles in a certain class that having a second countable locally compact Hausdorff base space and separable fibers implies the separability of the Banach space of the all sections that vanish at infinity. In the reverse direction, ... More

Abstract Lorentz spaces and Köthe dualityFeb 05 2018Given a fully symmetric Banach function space $E$ and a decreasing positive weight $w$ on $I = (0, a)$, $0 < a \le \infty $, the generalized Lorentz space ${\Lambda}_{E,w}$ is defined as the symmetrization of the canonical copy $E_w$ of $E$ on the measure ... More

On embeddings between spaces of functions of generalized bounded variationFeb 05 2018In this note, we aim to establish a number of embeddings between various function spaces that are frequently considered in the theory of Fourier series. More specifically, we give sufficient conditions for the embeddings $\Phi V[h]\subseteq \Lambda\text{BV}^{(p_n\uparrow ... More

Dunkl-Schrödinger operatorsFeb 05 2018In this paper, we consider the Schr\"odinger operators $L_k=-\Delta_k+V$, where $\Delta_k$ is the Dunkl-Laplace operator and $V$ is a non-negative potential on $R^d$. We establish that $L_k $ is essentially self-adjoint on $C_0^\infty$. In particular, ... More

A study on downward half Cauchy sequencesFeb 05 2018In this paper, we introduce and investigate the concepts of down continuity and down compactness. A real valued function $f$ on a subset $E$ of $\R$, the set of real numbers is down continuous if it preserves downward half Cauchy sequences, i.e. the sequence ... More

On the geometry of the Banach spaces $C([0,α]\times K)$ for some scattered $\clubsuit$-compactaFeb 04 2018For some non-metrizable scattered $K$ compacta, constructed under the assumption of the Ostaszewski's $\clubsuit$-principle, we study the geometry of the Banach spaces of the form $C(M\times K)$ where $M$ is a countable compact metric space. In particular, ... More

Reduced commutativity of moduli of operatorsFeb 03 2018In this paper, we investigate the question of when the equations $A^{*s}A^{s}=(A^{*}A)^{s}$ for all $s \in S$, where $S$ is a finite set of positive integers, imply the quasinormality or normality of $A$. In particular, it is proved that if $S=\{p,m,m+p,n,n+p\}$, ... More

Bernstein functions of several semigroup generators on Banach spaces under bounded perturbations. IIFeb 03 2018The paper deals with multidimensional Bochner-Phillips functional calculus. In the previous paper by the author bounded perturbations of Bernstein functions of several commuting semigroup generators on Banach spaces where considered, conditions for Lipschitzness ... More

Entropy numbers of finite-dimensional embeddingsFeb 02 2018Entropy numbers and covering numbers of sets and operators are well known geometric notions, which found many applications in various fields of mathematics, statistics, and computer science. Their values for finite-dimensional embeddings $id:\ell_p^n\to ... More

Orthogonally additive polynomials on convolution algebras associated with a compact groupFeb 01 2018Let $G$ be a compact group, let $X$ be a Banach space, and let $P\colon L^1(G)\to X$ be an orthogonally additive, continuous $n$-homogeneous polynomial. Then we show that there exists a unique continuous linear map $\Phi\colon L^1(G)\to X$ such that $P(f)=\Phi ... More

Orthogonally additive polynomials on the algebras of approximable operatorsFeb 01 2018Let $X$ and $Y$ be Banach spaces, let $\mathcal{A}(X)$ stands for the algebra of approximable operators on $X$, and let $P\colon\mathcal{A}(X)\to Y$ be an orthogonally additive, continuous $n$-homogeneous polynomial. If $X^*$ has the bounded approximation ... More

Embeddings for spaces of Lorentz-Sobolev typeJan 31 2018The purpose of this paper is to characterize all embeddings for versions of Besov and Triebel-Lizorkin spaces where the underlying Lebesgue space metric is replaced by a Lorentz space metric. We include two appendices, one on the relation between classes ... More

Holomorphic operator valued functions generated by passive selfadjoint systemsJan 31 2018In this paper we study a class $\mathcal R\mathcal S(\mathfrak M)$ of operator functions that are holomorphic in the domain $\mathbb C\setminus\{(-\infty,-1]\cup [1,+\infty)\}$ and whose values are contractive operators in a Hilbert space $(\mathfrak ... More

On extreme contractions between real Banach spacesJan 30 2018We completely characterize extreme contractions between two-dimensional strictly convex and smooth real Banach spaces, perhaps for the very first time. In order to obtain the desired characterization, we introduce the notions of (weakly) compatible point ... More

A characterization of nonnegativity relative to proper conesJan 30 2018Feb 06 2018Let $A$ be an $m \times n$ matrix with real entries. Given two proper cones $K_1$ and $K_2$ in $\mathbb{R}^n$ and $\mathbb{R}^m$, respectively, we say that $A$ is nonnegative (relative to $K_1$ and $K_2$) if $A(K_1) \subseteq K_2$. $A$ is said to be semipositive ... More

Bounded multiplicative Toeplitz operators on sequence spacesJan 29 2018In this paper, we study the linear mapping which sends the sequence $x=(x_n)_{n \in \mathbb{N}}$ to $y=(y_n)_{n \in \mathbb{N}}$ where $y_n = \sum_{k=1}^\infty f(n/k)x_k$ for $f: \mathbb{Q}^+ \to \mathbb{C}$. This operator is the multiplicative analogue ... More

Operational calculus for Fourier transform on the group $GL(2,R)$Jan 29 2018Consider the Fourier transform on the group $GL(2,R)$ of real $2\times 2$-matrices. We show that Fourier-images of polynomial differential operators on $GL(2,R)$ are differential-difference operators with coefficients meromorphic in parameters of representations. ... More

Kirk's Fixed Point Theorem in Complete Random Normed modulesJan 29 2018Recently, stimulated by financial applications and $L^0$--convex optimization, Guo, et.al introduced the notion of $L^0$--convex compactness for an $L^0$--convex subset of a Hausdorff topological module over the topological algebra $L^0(\mathcal{F},K)$, ... More

A Balian-Low Theorem for SubspacesJan 28 2018We extend the Balian-Low theorem to Gabor subspaces of $L^2(\mathbb R)$ by involving the concept of additional time-frequency shift invariance. We prove that if a Gabor system on a lattice of rational density is a Riesz sequence generating a subspace ... More

Duality of Bochner spacesJan 27 2018Feb 01 2018We construct the generalized Lebesgue--Bochner spaces $L^p(\mu,\varPi)$ for positive measures $\mu$ and for suitable real or complex topological vector spaces $\varPi$ so that for $1<p<+\infty$ and Banachable $\varPi$ with separable topology the strong ... More

After Plancherel formulaJan 26 2018We discuss two topics related to Fourier transforms on Lie groups and on homogeneous spaces: the operational calculus and the Gelfand--Gindikin problem (program) about separation of non-uniform spectra. Our purpose is to indicate some non-solved problems ... More

Concentration without measureJan 26 2018Although there doesn't exist the Lebesgue measure in the ball $M$ of $C[0,1]$ with $p-$norm, the average values (expectation) $EY$ and variance $DY$ of some functionals $Y$ on $M$ can still be defined through the procedure of limitation from finite dimension ... More

An inverse result of approximation by sampling Kantorovich seriesJan 26 2018In the present paper, an inverse result of approximation, i.e., a saturation theorem for the sampling Kantorovich operators is derived, in the case of uniform approximation for uniformly continuous and bounded functions on the whole real line. In particular, ... More

New results about some inequalities for operator meansJan 25 2018Feb 05 2018New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator P\'olya-Szeg\"o inequality to arbitrary operator means. Furthermore, ... More

Local extension property for finite height spacesJan 25 2018We introduce a new technique for the study of the local extension property (LEP) for boolean algebras and we use it to show that the clopen algebra of every compact Hausdorff space $K$ of finite height has LEP. This implies, under appropriate additional ... More

Limit Operators, Compactness and Essential Spectra on Bounded Symmetric DomainsJan 25 2018This paper is a follow-up to a recent article about the essential spectrum of Toeplitz operators acting on the Bergman space over the unit ball. As mentioned in the said article, some of the arguments can be carried over to the case of bounded symmetric ... More

On Weak Supercyclicity IJan 24 2018This paper provides conditions (i) to distinguish weak supercyclicity form supercyclicity for operators acting on normed and Banach spaces, and also (ii) to ensure when weak supercyclicity implies weak stability.

Fixed point, Gregus-Ciric-contraction, monotone mappings, weighted graphJan 23 2018In this paper, we introduce the concept of monotone Gregus-\'Ciri\'c-contraction mappings in weighted digraphs. Then we establish a fixed point theorem for monotone Gregus-\'Ciri\'c-contraction mappings defined in convex weighted digraphs.

Sharp comparison of moments and the log-concave moment problemJan 23 2018This article investigates sharp comparison of moments for various classes of random variables appearing in a geometric context. In the first part of our work we find the optimal constants in the Khintchine inequality for random vectors uniformly distributed ... More

Multivariable Bergman shifts and Wold decompositionsJan 23 2018Let $H_m(\mathbb B)$ be the analytic functional Hilbert space on the unit ball $\mathbb B \subset \mathbb C^n$ with reproducing kernel $K_m(z,w) = (1 - \langle z,w \rangle)^{-m}$. Using algebraic operator identities we characterize those commuting row ... More

A note on Saint Raymond's Theorem about the weak compactness of sublevel setsJan 23 2018In this work we prove that if $X$ is a complete locally convex space and $f:X\to \mathbb{R}\cup \{+\infty \}$ is a function such that $f-x^\ast$ attains its minimum for every $x^\ast \in U$, where $U$ is an open set with respect to the Mackey topology. ... More

Optimal Convergence for Distributed Learning with Stochastic Gradient Methods and Spectral-Regularization AlgorithmsJan 22 2018We study generalization properties of distributed algorithms in the setting of nonparametric regression over a reproducing kernel Hilbert space (RKHS). We first investigate distributed stochastic gradient methods (SGM), with mini-batches and multi-passes ... More

On the Existence of Normal Square and Nth Roots of OperatorsJan 21 2018Jan 24 2018The primary purpose of this paper is to show the existence of normal square and nth roots of some classes of bounded operators on Hilbert spaces. Two interesting simple results hold. Namely, under simple conditions we show that if any operator $T$ is ... More

Global and Concrete Quantizations on General Type I GroupsJan 21 2018In recent papers and books, a global quantization has been developed for {\it unimodular} groups of type I\,. It involves operator-valued symbols defined on the product between the group $\G$ and its unitary dual $\wG$\,, composed of equivalence classes ... More

Nonlinear operations on a class of modulation spacesJan 21 2018We discuss when the nonlinear operation $f\mapsto F(f)$ maps the modulation space $M^{p,q}_s(\mathbb{R}^n)$ ($1 \leq p,q \leq \infty$) to the same space again. It is known that $M^{p,q}_s(\mathbb{R}^n)$ is a multiplication algebra when $s > n-n/q$, hence ... More

A general approach to approximation theory of operator semigroupsJan 21 2018We develop a general, functional calculus approach to approximation of $C_0$-semigroups on Banach spaces by bounded completely monotone functions of their generators. The approach comprises most of well-known approximation formulas, yields optimal convergence ... More

Optimal Rates for Spectral-regularized Algorithms with Least-Squares Regression over Hilbert SpacesJan 20 2018In this paper, we study regression problems over a separable Hilbert space with the square loss, covering non-parametric regression over a reproducing kernel Hilbert space. We investigate a class of spectral-regularized algorithms, including ridge regression, ... More

Vector valued Hardy spacesJan 20 2018The Hardy space $H^{p}$ of vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ and with values in Banach space are defined. Vector valued analytic functions in tube domains in $\mathbb{C}^{n}$ with values in Hilbert space and which have ... More

Coupled Fixed Points of monotone mappings in a metric space with a graphJan 20 2018In this work, we define the concept of mixed $G$-monotone mappings defined on a metric space endowed with a graph. Then we obtain sufficient conditions for the existence of coupled fixed points for such mappings when a weak contractivity type condition ... More

Mann Iteration Process for Monotone Nonexpansive Mappings with a GraphJan 20 2018Let $(X,\|.\|)$ be a Banach space. Let $C$ be a nonempty, bounded, closed, and convex subset of $X$ and $T: C \rightarrow C$ be a $G$-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by $$x_{n+1} = t_n ... More

Linear space properties of $H^p$ spaces of Dirichlet seriesJan 19 2018We study $H^p$ spaces of Dirichlet series, called $\mathcal{H}^p$, for the range $0<p< \infty$. We begin by showing that two natural ways to define $\mathcal{H}^p$ coincide. We then proceed to study some linear space properties of $\mathcal{H}^p$. More ... More

Eventually Entanglement Breaking MapsJan 17 2018We analyze certain class of linear maps on matrix algebras that become entanglement breaking after composing a finite or infinite number of times with themselves. This means that the Choi matrix of the iterated linear map becomes separable in the tensor ... More

Graph Laplace and Markov operators on a measure spaceJan 13 2018The main goal of this paper is to build a measurable analogue to the theory of weighted networks on infinite graphs. Our basic setting is an infinite $\sigma$-finite measure space $(V, \mathcal B, \mu)$ and a symmetric measure $\rho$ on $(V\times V, \mathcal ... More

Determining Projection Constants of Univariate Polynomial SpacesJan 12 2018The long-standing problem of minimal projections is addressed from a computational point of view. Techniques to determine bounds on the projection constants of univariate polynomial spaces are presented. The upper bound, produced by a linear program, ... More

A relative bicommutant theorem: the stable case of Pedersen's questionJan 11 2018In 1976, D. Voiculescu proved that every separable unital sub-C*-algebra of the Calkin algebra is equal to its (relative) bicommutant. In his minicourse (see reference), G. Pedersen asked in 1988 if Voiculescu's theorem can be extended to a simple corona ... More

Homogeneous length functions on groupsJan 11 2018A pseudo-length function defined on an arbitrary group $G = (G,\cdot,e, (\,)^{-1})$ is a map $\ell : G \to [0,+\infty)$ obeying $\ell(e)=0$, the symmetry property $\ell(x^{-1}) = \ell(x)$, and the triangle inequality $\ell(xy) \leqslant \ell(x) + \ell(y)$ ... More

Multiplication of Distributions and Nonperturbative Calculations of Transition ProbabilitiesJan 10 2018In a mathematical context in which one can multiply distributions the "`formal"' nonperturbative canonical Hamiltonian formalism in Quantum Field Theory makes sense mathematically, which can be understood a priori from the fact the so called "`infinite ... More

Smooth Version of Johnson's Problem Concerning Derivations of Group AlgebrasJan 10 2018A description of the algebra of outer derivations of a group algebra of a finitely presented discrete group is given in terms of the Cayley complex of the groupoid of the adjoint action of the group. This task is a smooth version of Johnson's problem ... More

Reducible characteristic cycles of Harish-Chandra modules for $\mathrm{U}(p,q)$ and the Kashiwara-Saito singularityJan 10 2018We give examples of reducible characteristic cycles for irreducible Harish-Chandra modules for $\mathrm{U}(p,q)$ by analyzing a four-dimensional singular subvariety of $\mathbb{C}^8$. We relate this singularity to the Kashiwara-Saito singularity arising ... More

The Choquet integral with respect to fuzzy measures and applicationsJan 10 2018Fuzzy measures and Choquet asymmetric integral are considered here. As an application to economics some Core-Walras results are given.

The Petersen graph has no quantum symmetryJan 09 2018Jan 17 2018In 2007, Banica and Bichon asked whether the well-known Petersen graph has quantum symmetry. In this article, we show that the Petersen graph has no quantum symmetry, i.e. the quantum automorphism group of the Petersen graph is its usual automorphism ... More

Wulff shapes and a characterization of simplices via a Bezout type inequalityJan 08 2018Inspired by a fundamental theorem of Bernstein, Kushnirenko, and Khovanskii we study the following Bezout type inequality for mixed volumes $$ V(L_1,\dots,L_{n})V_n(K)\leq V(L_1,K[{n-1}])V(L_2,\dots, L_{n},K). $$ We show that the above inequality characterizes ... More

Fixed Points of anti-attracting maps and Eigenforms on FractalsJan 08 2018An important problem in analysis on fractals is the existence of a self-similar energy on finitely ramified fractals. The self-similar energies are constructed in terms of eigenforms, that is, eigenvectors of a special nonlinear operator. Previous results ... More

On Absolutely Norm attaining OperatorsJan 08 2018We give necessary and sufficient conditions for a bounded operator defined between complex Hilbert spaces to be absolutely norm attaining. We discuss structure of such operators in the case of self-adjoint and normal operators separately. Finally, we ... More

On the existence of an ultra central approximate identity for certain semigroup algebrasJan 05 2018In this paper we characterize the existance of an ultra central approximate identity for $\ell^{1}(S)$, where $S$ is a uniformly locally finite inverse semigroup. As an application, for the Brandt semigroup $S=M^{0}(G,I)$ over a non-empty set $I$, we ... More

Covariant Schrödinger semigroups on noncompact Riemannian manifoldsJan 04 2018This monograph develops the theory of covariant Schr\"odinger semigroups acting on sections of vector bundles over noncompact Riemannian manifolds from scratch. Contents: I. Sobolev spaces on vector bundles II. Smooth heat kernels on vector bundles III. ... More

Frobenius Theorem in Banach SpaceJan 04 2018Let $\Lambda$ be an open set in Banach space $E$, $M(x)$ for $x\in \Lambda$ a subspace in $E$, and $\mathcal F=\{M(x)\}_{x\in\Lambda}$. In this paper, we introduce the concept of the co-final set $J(x_0,E_*)$ for $\mathcal F$ at $x_0\in \Lambda$, then ... More

A new representation of Hankel operators and its spectral consequencesJan 02 2018We describe a new representation of Hankel operators $H$ as pseudo-differential operators $A$ in the space of functions defined on the whole axis. The amplitudes of such operators $A$ have a very special structure: they are products of functions of a ... More

Truncated Calderón-Zygmund operators without extra cancellation propertyDec 30 2017Jan 23 2018It is proved that the truncated Calder\'on-Zygmund operator $T_D$ with the even kernel is bounded on on the Campanato space $\mathcal{C}_\omega(D),$ provided $D$ is a $C^{1,\widetilde{\omega}}$-smooth domain with $\widetilde{\omega}(x)= \omega(x)(\int_x^1 ... More

Moment measures and stability for Gaussian inequalitiesDec 30 2017Let $\gamma$ be the standard Gaussian measure on $\mathbb{R}^n$ and let $\mathcal{P}_{\gamma}$ be the space of probability measures that are absolutely continuous with respect to $\gamma$. We study lower bounds for the functional $\mathcal{F}_{\gamma}(\mu) ... More

$\mathcal{S}^2$-differentiability and extension of the Koplienko trace formulaDec 29 2017Let $A$ be a selfadjoint operator in a separable Hilbert space, $K$ a selfadjoint Hilbert-Schmidt operator, and $f\in C^n(\mathbb{R})$. We establish that $\varphi(t)=f(A+tK)-f(A)$ is $n$-times continuously differentiable on $\mathbb{R}$ in the Hilbert-Schmidt ... More

Spectral properties of the 2+1 fermionic trimer with contact interactionsDec 29 2017Jan 08 2018We qualify the main features of the spectrum of the Hamiltonian of point interaction for a three-dimensional quantum system consisting of three point-like particles, two identical fermions, plus a third particle of different species, with two-body interaction ... More

Existence and stability of periodic solutions in a neural field equationDec 27 2017We study the existence and linear stability of stationary periodic solutions to a neural field model, an intergo-differential equation of the Hammerstein type. Under the assumption that the activation function is a discontinuous step function and the ... More

Stability properties of the differential process generated by complex interpolationDec 27 2017We obtain stability results for the bounded, trivial or singular character of the differential process of Rochberg and Weiss associated to complex interpolation of an analytic family of Banach spaces. Among other results, it is proved that there is global ... More

On weighted polynomial approximationDec 26 2017Let $\varPhi:{\mathbb R}^n \to [1, \infty)$ be a semi-continuous from below function such that $\lim \limits_{x \to \infty} \displaystyle \frac {\ln \varPhi(x)} {\Vert x \Vert} = +\infty$. It is shown that polynomials are dense in $C_{\varPhi}({\mathbb ... More

A priori estimates for the Fitzpatrick functionDec 26 2017New perspectives, proofs, and some extensions of known results are presented concerning the behavior of the Fitzpatrick function of a monotone type operator in the general context of a locally convex space.

On embeddings of locally finite metric spaces into $\ell_p$Dec 21 2017It is known that if finite subsets of a locally finite metric space $M$ admit $C$-bilipschitz embeddings into $\ell_p$ $(1\le p\le \infty)$, then for every $\epsilon>0$, the space $M$ admits a $(C+\epsilon)$-bilipschitz embedding into $\ell_p$. The goal ... More

On $\ell^1$-regularization under continuity of the forward operator in weaker topologiesNov 23 2017Our focus is on the stable approximate solution of linear operator equations based on noisy data by using $\ell^1$-regularization as a sparsity-enforcing version of Tikhonov regularization. We summarize recent results on situations where the sparsity ... More

A special class of fuzzy measures: Choquet integral and applicationsNov 23 2017Core of an economy and Walras equilibria are considered for a product space $X \times [0,1]$ using the Choquet integral with respect to a fuzzy measure.

Radial Toeplitz operators on the weighted Bergman spaces of Cartan domainsOct 31 2017Let $D$ be an irreducible bounded symmetric domain with biholomorphism group $G$ with maximal compact subgroup $K$. For the Toeplitz operators with $K$-invariant symbols we provide explicit simultaneous diagonalization formulas on every weighted Bergman ... More

Moment infinitely divisible weighted shiftsOct 29 2017We say that a weighted shift $W_\alpha$ with (positive) weight sequence $\alpha: \alpha_0, \alpha_1, \ldots$ is {\it moment infinitely divisible} (MID) if, for every $t > 0$, the shift with weight sequence $\alpha^t: \alpha_0^t, \alpha_1^t, \ldots$ is ... More

Weyl's Theorem for pairs of commuting hyponormal operatorsOct 29 2017Let $\mathbf{T}$ be a pair of commuting hyponormal operators satisfying the so-called quasitriangular property $$ \textrm{dim} \; \textrm{ker} \; (\mathbf{T}-\boldsymbol\lambda) \ge \textrm{dim} \; \textrm{ker} \; (\mathbf{T} - {\boldsymbol\lambda})^*), ... More

A new approach to the nonsingular cubic binary moment problemOct 29 2017We present an alternative solution to nonsingular cubic moment problems, using techniques that are expected to be useful for higher-degree truncated moment problems. In particular, we apply the theory of recursively determinate moment matrices to deal ... More

Lamé Parameter Estimation from Static Displacement Field Measurements in the Framework of Nonlinear Inverse ProblemsOct 28 2017Jan 19 2018We consider a problem of quantitative static elastography, the estimation of the Lam\'e parameters from internal displacement field data. This problem is formulated as a nonlinear operator equation. To solve this equation, we investigate the Landweber ... More

Sharp trace Gagliardo-Nirenberg-Sobolev inequalities for convex cones, and convex domainsOct 23 2017We find a new sharp trace Gagliardo-Nirenberg-Sobolev inequality on convex cones, aswell as a weighted sharp trace Sobolev inequality on epigraphs of convex functions. This is done by using a generalized Borell-Brascamp-Lieb inequality, coming from the ... More

Optimal Rates for Learning with Nyström Stochastic Gradient MethodsOct 21 2017In the setting of nonparametric regression, we propose and study a combination of stochastic gradient methods with Nystr\"om subsampling, allowing multiple passes over the data and mini-batches. Generalization error bounds for the studied algorithm are ... More

Derivations of Group AlgebrasAug 16 2017In the paper, a method of describing the outer derivations of the group algebra of a finitely presentable group is given. The description of derivations is given in terms of characters of the groupoid of the adjoint action of the group.

Cyclicity in $\ell^p$ spaces and zero sets of the Fourier transformsJul 31 2017Jan 10 2018We study the cyclicity of vectors $u$ in $\ell^p(\mathbb{Z})$. It is known that a vector $u$ is cyclic in $\ell^2(\mathbb{Z})$ if and only if the zero set, $\mathcal{Z}(\widehat{u})$, of its Fourier transform, $\widehat{u}$, has Lebesgue measure zero ... More

A non-linear Bishop-Phelps-Bollobás type theoremJul 21 2017The main aim of this paper is to prove a Bishop-Phelps-Bollob\'as type theorem on the unital uniform algebra A_{w^*u}(B_{X^*}) consisting of all w^*-uniformly continuous functions on the closed unit ball B_{X^*} which are holomorphic on the interior of ... More

Fourth moment theorems on the Poisson space in any dimensionJul 06 2017We extend to any dimension the quantitative fourth moment theorem on the Poisson setting, recently proved by C. D\"obler and G. Peccati (2017). In particular, by adapting the exchangeable pairs couplings construction introduced by I. Nourdin and G. Zheng ... More

Generalization Properties of Doubly Online Learning AlgorithmsJul 03 2017Doubly online learning algorithms are scalable kernel methods that perform very well in practice. However, their generalization properties are not well understood and their analysis is challenging since the corresponding learning sequence may not be in ... More

Quantum Symmetries of Graph C*-AlgebrasJun 27 2017The study of graph C*-algebras has a long history in operator algebras. Surprisingly, their quantum symmetries have never been computed so far. We close this gap by proving that the quantum automorphism group of a finite, directed graph without multiple ... More

Aluthge transforms of 2-variable weighted shiftsJun 11 2017We introduce two natural notions of multivariable Aluthge transforms (toral and spherical), and study their basic properties. In the case of 2-variable weighted shifts, we first prove that the toral Aluthge transform does not preserve (joint) hyponormality, ... More

$M$-ideal properties in Orlicz-Lorentz spacesMay 30 2017Jun 28 2017We provide explicit formulas for the norm of bounded linear functionals on Orlicz-Lorentz function spaces $\Lambda_{\varphi,w}$ equipped with two standard Luxemburg and Orlicz norms. Any bounded linear functional is a sum of regular and singular functionals, ... More

Dirichlet-to-Neumann or Poincaré-Steklov operator on fractals described by d -setsMay 26 2017Jul 05 2017In the framework of the Laplacian transport, described by a Robin boundary value problem in an exterior domain in $\mathbb{R}^n$, we generalize the definition of the Poincar\'e-Steklov operator to $d$-set boundaries, $n-2< d<n$, and give its spectral ... More